GrizzlyChicken
how do you solve 16^(-3/4) without a calculator?
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009infinity
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split the powers and then do individually
GrizzlyChicken
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what do you mean by split the powers?
009infinity
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do u got it
GrizzlyChicken
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no, im lost where -3 is multiplyed by 6 and then the ^1/4 part
009infinity
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ok i explain in steps
theEric
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(-3) means \[\frac{1}{16^3}\] and (1/4) means \[\sqrt[4]{16}\] right?
So, since you're doing both to the 16...
it can be written as
\[\frac{1}{\sqrt[4]{16^3}}\]
or
\[\frac{1}{\sqrt[4]{16}^3}\]
GrizzlyChicken
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that makes sense so far
theEric
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Now, one looks much more easy to solve than the other, even though they are the same thing.
009infinity
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the power is -3/4
base is 16
now 16^-3 . 16^1/4=1/(16)^3.\[\sqrt[4]{16}\]
GrizzlyChicken
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how does \[\sqrt[4]{16^3}\] turn into 8?
GrizzlyChicken
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i know the answer is 1/8
GrizzlyChicken
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\[\sqrt[4]{4096}\]
GrizzlyChicken
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nvm
theEric
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I would look at it the other way - just to avoid that huge number \[16^3\].
theEric
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\[\frac{1}{\sqrt[4]{16}^3}\]
theEric
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So it's like
\[\frac{1}{(\sqrt[4]{16})^3}\]
theEric
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And what is \[\sqrt[4]{16}\]?
theEric
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Guess :P
theEric
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It's a nice number.
GrizzlyChicken
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2
GrizzlyChicken
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sorry, i was afk for a while
GrizzlyChicken
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then 2^3 is 8
GrizzlyChicken
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so 1/8
GrizzlyChicken
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thanks!
theEric
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Understood! Thank you! And you're welcome!